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Nonlinear PDE fitting to Data


   I have a data set that I want to fit it to a nonlinear PDE which is 
solved numerically.
   I tried to fit it by interpolating my numerical solution for each 
fitting parameter, which I have roughly 3 of them.  It means that I 
have to run my numerical program for each parameter, interpolate, and 
then fit the interpolating function to the data set.
Mathematica keep running out of memory on me.
   Anyone has any examples or suggestions on this problem?

Thank you very much,

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